Related papers: A generalization of the line translation theorem

This paper proves a deformation circle pattern theorem, which gives a complete description of those circle patterns with interstices in terms of the combinatorial type, the exterior intersections angles and the conformal structures of…

Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the changes under the variation of parameters lead to rather…

The classical Mazur-Ulam theorem establishes that every surjective isometry between normed real vector spaces is an affine transformation. In various applied mathematical settings, however, one encounters maps that preserve distances not…

The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including…

We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…

We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…

We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions.…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

We present a unified theory to treat conservation laws in light-matter interactions. It can be used to describe and engineer the transfer of any measurable property from the electromagnetic field to any object. The theory allows to…

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

The aim of this paper is to establish and study the linear canonical Dunkl wavelet transform. We begin by introducing the generalized translation operator and generalized convolution product for the linear canonical Dunkl transform and we…

We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as…

In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…

The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The…

We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together…

Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…

Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is…

A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…

The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous…